Problem: Express your answer as a mixed number simplified to lowest terms. $13\dfrac{1}{6}-5\dfrac{4}{5} = {?}$
Answer: Find a common denominator for the fractions: $= {13\dfrac{5}{30}}-{5\dfrac{24}{30}}$ Convert ${13\dfrac{5}{30}}$ to ${12 + \dfrac{30}{30} + \dfrac{5}{30}}$ So the problem becomes: ${12\dfrac{35}{30}}-{5\dfrac{24}{30}}$ Separate the whole numbers from the fractional parts: $= {12} + {\dfrac{35}{30}} - {5} - {\dfrac{24}{30}}$ Bring the whole numbers together and the fractions together: $= {12} - {5} + {\dfrac{35}{30}} - {\dfrac{24}{30}}$ Subtract the whole numbers: $=7 + {\dfrac{35}{30}} - {\dfrac{24}{30}}$ Subtract the fractions: $= 7+\dfrac{11}{30}$ Combine the whole and fractional parts into a mixed number: $= 7\dfrac{11}{30}$